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A199532
Number of -n..n arrays x(0..4) of 5 elements with zero sum and no two consecutive zero elements.
1
32, 320, 1324, 3734, 8470, 16682, 29750, 49284, 77124, 115340, 166232, 232330, 316394, 421414, 550610, 707432, 895560, 1118904, 1381604, 1688030, 2042782, 2450690, 2916814, 3446444, 4045100, 4718532, 5472720, 6313874, 7248434, 8283070
OFFSET
1,1
COMMENTS
Row 5 of A199530.
LINKS
FORMULA
Empirical: a(n) = (115/12)*n^4 + (115/6)*n^3 + (41/12)*n^2 - (1/6)*n.
Conjectures from Colin Barker, May 15 2018: (Start)
G.f.: 2*x*(16 + 80*x + 22*x^2 - 3*x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
EXAMPLE
Some solutions for n=5:
..2....1....3...-5....1....0....5....5...-3....4...-5....1...-5...-2....0...-1
.-5...-2....4....4....4...-1...-3....0...-1...-3....1....0....3....3....1....5
.-4...-2...-4....1....3....1...-3...-2....2...-5....2...-5...-2...-3...-3....3
..3....4...-1...-2...-5....3...-1...-1...-3...-1....2....4...-1...-2...-3...-3
..4...-1...-2....2...-3...-3....2...-2....5....5....0....0....5....4....5...-4
CROSSREFS
Cf. A199530.
Sequence in context: A050279 A096764 A256802 * A165004 A244867 A173952
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 07 2011
STATUS
approved